Stability Analysis of Networked Control Systems Using a Switched Linear Systems Approach

Abstract

International audienceIn this paper, we study the stability of networked control systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, and communication constraints. Communication constraints impose that, per transmission, only one node can access the network and send its information. The order in which nodes send their information is orchestrated by a network protocol, such as, the Round-Robin (RR) and the Try-Once-Discard (TOD) protocol. In this paper, we generalize the mentioned protocols to novel classes of so-called "periodic" and "quadratic" protocols. By focusing on linear plants and controllers, we present a modeling framework for NCSs based on discrete-time switched linear uncertain systems. This framework allows the controller to be given in discrete time as well as in continuous time. To analyze stability of such systems for a range of possible transmission intervals and delays, with a possible nonzero lower bound, we propose a new procedure to obtain a convex overapproximation in the form of a polytopic system with norm-bounded additive uncertainty. We show that this approximation can be made arbitrarily tight in an appropriate sense. Based on this overapproximation, we derive stability results in terms of linear matrix inequalities (LMIs). We illustrate our stability analysis on the benchmark example of a batch reactor and show how this leads to tradeoffs between different protocols, allowable ranges of transmission intervals and delays. In addition, we show that the exploitation of the linearity of the system and controller leads to a significant reduction in conservatism with respect to existing approaches in the literature

Stability analysis of networked control systems: A sum of squares approach

“…[5]- [7], [10], [11], [14], [25], [26], which applies to linear plants and linear controllers and is based on exact discretization of the NCS between two transmission times. After a polytopic overapproximation step, robust stability analysis methods are used to obtain LMI-based conditions for stability of the NCS.…”

Robust Stability of Networked Control Systems with Communication Constraints

“…Recently, much attention has been focused on analysis and synthesis of networked control systems NCSs, and many stability criteria can be traced in [22], [23]. In [24], an NCS with limited bandwidths was modeled as a switched system with time-varying delay, and a similar switching law had been used to stabilize the NCS, which shows that the result given in this paper may also be applicable to such system.…”

Bandwidth Reduction and Convergence Analysis of Extremum Seeking Control with Feedback Encoding

“…In a networked control system (NCS) that is packet switched, when a periodically sampled variable is transmitted over the communication network it can be subject to the congestion related issues such as delay, delay variation, and packet drops as reported in Zampieri (2008), Donkers et al (2011), andPremaratne (2014). In Wu et al (2013), it is demonstrated that congestion can lead to increased packet drops.…”

“…From Assumption 4, the ESC scheme of equation (1) need not be considered as a discrete system as in Choi et al (2002). Assumptions 5 and 6 are necessary to neglect any effect due to delay and delay variation (jitter), which is inevitable in a packet switched communication network according to the results of Zampieri (2008), Donkers et al (2011), andPremaratne (2014).…”